lmomco (version 0.6)

cdfpe3: Cumulative Distribution Function of the Pearson Type III Distribution

Description

This function computes the cumulative probability or nonexceedance probability of the Pearson Type III distribution given parameters ($\xi$, $\alpha$, and $\gamma$) of the distribution computed by parpe3. The cumulative distribution function of the distribution is

$$F(x) = \frac{G\left(\alpha,\frac{x - \xi}{\gamma}\right)}{\Gamma(\alpha)} \mbox{,}$$

where $F(x)$ is the nonexceedance probability for quantile $x$, $G$ is the incomplete gamma function, $\Gamma$ is the gamma function, $\xi$ is a location parameter, $\alpha$ is a scale parameter, and $\gamma$ is a shape parameter.

Usage

cdfpe3(x, para)

Arguments

x

A real value.

para

The parameters from parpe3 or similar.

Value

• Nonexceedance probability ($F$) for $x$.

References

Hosking, J.R.M., 1990, L-moments---Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105--124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis---An approach based on L-moments: Cambridge University Press.

See Also

quape3, parpe3

Examples

lmr <- lmom.ub(c(123,34,4,654,37,78))
  cdfpe3(50,parpe3(lmr))